Galadriel destroyed the enemy fortress, and she was also known for fighting against Fëanor and Sauron in earlier ages. So in this sense, Galadriel was a warrior in that she waged war against evil, and was an active participant in current events of Middle-earth. This allowed her to fight head to head with other characters.
Qualities of a Warrior
Her mother-name was Nerwen (‘man-maiden’), and she grew to be tall beyond the measure even of the women of the Noldor; she was strong of body, mind, and will, a match for both the loremasters and the athletes of the Eldar in the days of their youth,
Unfinished Tales (p. 221).
Letter 348 says that Galadriel was “of Amazonian disposition and bound up her hair as a crown when taking part in athletic feats.” (L 348) However, it is unknown what types of feats one would expect from her, though it implies that she was tall and athletic. This Amazonian disposition, however, hints to many that she would be a warrior and have warrior-like qualities.
While she wasn’t exactly depicted with a sword in Tolkien’s writings (as opposed to her having one in the Rings of Power), she held a lot of powers that made her able to fight without being a physical warrior, which started from her desire to remain in Middle-earth in the First Age.
Refusal to leave
In Doriath Galadriel met Celeborn, but she refused to go west to Eressëa, and did not go west at the Downfall of Melkor as a result of her love of Celeborn and also with some pride of her own, as she was one of those eager to adventure in Middle-earth.
Galadriel had good intentions to refuse to leave, earlier in the same tale, it was mentioned that she “joined the rebellion against the Valar who commanded them to stay; and once she set foot upon that road of exile she would not relent, but rejected the last message of the Valar, and came under the Doom of Mandos.” (Unfinished Tales, “The History of Galadriel and Celeborn”)
While Tolkien marks her as a penitent, he also emphasizes that she didn’t commit any evil deeds in this decision, as she was mainly motivated by the revolts of Fëanor.
Galadriel was ‘unstained’: she had committed no evil deeds. She was an enemy of Fëanor. She did not reach Middle-earth with the other Noldor, but independently. Her reasons for desiring to go to Middle-earth were legitimate, and she would have been permitted to depart, but for the misfortune that before she set out the revolt of Fëanor broke out, and she became involved in the desperate measures of Manwe, and the ban on all emigration. (Letter 353)
However, in a very late note, Galadriel’s conduct at the time of rebellion shows that he “emphasized the commanding stature of Galadriel already in Valinor, the equal if unlike in endowments of Fëanor; and it is said here that so far from joining in Fëanor’s revolt she was in every way opposed to him. She did indeed wish to depart from Valinor and to go into the wide world of Middle-earth for the exercise of her talents; for ‘being brilliant in mind and swift to anger she had early absorbed all of what she was capable of the teaching which the Valar thought fit to the Eldar,’ and she felt confined in the tutelage of Aman.” (Unfinished Tales)
This desire would be known to Manwë, and Galadriel would first go to her mother’s kindred in Alqualondë, where she would meet Celeborn, a Telerin prince, and they would build the ship and sail it to Middle-earth.
“They were about to seek leave from the Valar for their venture when Melkor fled from Valor and returning with Ungoliant destroyed the light of the Trees.”
Fëanor
She was also moved by her desire to follow Fëanor even after the assault upon the Teleri. “Her pride was unwilling to return, a defeated suppliant for pardon; but now she burned with desire to follow Fëanor with her anger to whatever lands he might come, and to thwart him in all ways that she could. Pride still moved her when, at the end of the Elder Days after the final overthrow of Morgoth, she refused the pardon of the Valar for all who had fought against him, and remained in Middle-earth.” (Unfinished Tales, “The History of Galadriel and Celeborn”)
However, in the Silmarillion, it was told that Galadriel was eager to leave Valinor, without swearing any oath, “but the words of Fëanor concerning Middle-earth had kindled in her heart, for she yearned to see the wide unguarded lands and to rule there a realm at her own will.” (The Silmarillion)
Meanwhile, Galadriel would have no part in Fëanor’s revolt. She and Celeborn would fight heroically in defense of Alqualondë against the assault of the Noldor.
“Galadriel, despairing now of Valinor and horrified by the violence and cruelty of Fëanor, set sail into the darkness without waiting for Manwë’s leave, which would undoubtedly have been withheld in that hour, however legitimate her desire in itself. It was thus that she came under the ban set upon all departure, and Valinor was shut against her return.” (Unfinished Tales)
However, they would not join in the subsequent war against Angband, since they believed they were hopeless under the ban of the Valar. However, Galadriel and Celeborn were welcomed with joy in Middle-earth being the kin of Thingol.
Galadriel could sense that Fëanor’s greed would not change. This greed may be evident by his kinslaying at Alqualondë which she fought against as Fëanor led the Noldor.
Sauron
Galadriel would be aware of Sauron was left behind in the days of the captivity of Melkor, perceiving that “there was an evil controlling purpose abroad in the world, and that it seemed to proceed from a source further to the East, beyond Eriador and the Misty Mountains.” (UT)
Thus, Galadriel would go east in the Second Age, and entrusted the Dwarves as the finest warriors to fight against the Orcs.
Meanwhile, as her power grew, she would come into contact the Nandorin Realm of Lórinand on the other side of the Misty Mountains. There, she was successful in counteracting the machinations of Sauron while Gil-galad would shut him out in Lindon.
Sauron would pose as an emissary of the Valar, perceiving Galadriel to be his chief adversary. Sauron would be driven away after great slaughter at Sarn Ford and after Elrond and Gil-galad would become too strong for Sauron, Galadriel would be back in the narrative. She would develop a longing for the sea that she didn’t have before.
Proud, strong and self willed (commentary)
Galadriel is known to be “proud, strong, and self-willed,” which is commonly attributed to her being a warrior and having warrior-like qualities. However, that would also be in addition to her noble and generous spirit, resulting in her Amazonian Disposition, being a mentally and physically strong character.
“She was proud, strong, and selfwilled, as were all the descendants of Finwë save Finarfin; and like her brother Finrod, of all her kin the nearest to her heart, she had dreams of far lands and dominions that might be her own to order as she would without tutelage. Yet deeper still there dwelt in her the noble and generous spirit of the Vanyar, and a reverence of the Valar that she could not forget. …she had a marvelous gift of insight into the minds of others, but judged them with mercy and understanding, and she withheld her goodwill from none save only Fëanor. In him she perceived a darkness that she hated and feared, though she did not perceive that the shadow of the same evil had fallen upon the minds of all the Noldor, and upon her own.”
However, this trait is commonly attributed to her refusing to leave Middle-earth. She did, however, have a ban of the Valar.
The Exiles were allowed to return – save for a few chief actors in the rebellion, of whom at the time of The Lord of the Rings only Galadriel remained… Her personal ban was lifted in reward for her services against Sauron, and above all for her rejection of the temptation to take the Ring when offered to her. (Letter 297)
However, she was corrupted by Melkor in that Melkor would convince her and her people to take up swords in the Years of the Trees.
“Then with a cry [Feanor] ran from the Ring of Doom and fled into the night, distraught; for his father was dearer to him than the Light of Valinor or the peerless works of his hands: and who among sons, of Elves or of Men, have held their fathers of greater worth?” (HoME10)
One of her main powers was that of perception. As the bearer of the ring, Nenya, she was able to see evil before it happened, which she would do with Fëanor and Sauron and show her Amazonian dispositions as a warrior.
